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Civilians accounted for 21 of the dead; two of them were beheaded, according to the statement.

The real death toll could be a lot higher.

The group said it believes the actual casualty figure is twice the number documented, "because there is absolute secrecy on casualties and due to the difficulty of access to many areas and villages that have witnessed violent clashes and bombardment by the two sides."

Video from Kobani on Sunday showed a plume of smoke rising above the city, known in Arabic as Ayn al-Arab.

Most of the city's 200,000 people have fled across the border into neighboring Turkey.